Question: Simplify the following expression: $\dfrac{108n^3}{60n^5}$ You can assume $n \neq 0$.
Explanation: $ \dfrac{108n^3}{60n^5} = \dfrac{108}{60} \cdot \dfrac{n^3}{n^5} $ To simplify $\frac{108}{60}$ , find the greatest common factor (GCD) of $108$ and $60$ $108 = 2 \cdot 2 \cdot 3 \cdot 3 \cdot 3$ $60 = 2 \cdot 2 \cdot 3 \cdot 5$ $ \mbox{GCD}(108, 60) = 2 \cdot 2 \cdot 3 = 12 $ $ \dfrac{108}{60} \cdot \dfrac{n^3}{n^5} = \dfrac{12 \cdot 9}{12 \cdot 5} \cdot \dfrac{n^3}{n^5} $ $\phantom{ \dfrac{108}{60} \cdot \dfrac{3}{5}} = \dfrac{9}{5} \cdot \dfrac{n^3}{n^5} $ $ \dfrac{n^3}{n^5} = \dfrac{n \cdot n \cdot n}{n \cdot n \cdot n \cdot n \cdot n} = \dfrac{1}{n^2} $ $ \dfrac{9}{5} \cdot \dfrac{1}{n^2} = \dfrac{9}{5n^2} $